I am in New South Wales, Australia, and I have a fair understanding of how the system of birth registrations has worked in NSW. As I understand it, a similar set of principles operated/s at the GRO.
So this suggests to me that GRO should have just the ONE birth registered for the one person, but the GRO index itself can have several entries within that one INDEX under the possible surnames for that person.
So, in NSW in the late 19th and well into the 20th Century, a married couple's baby becomes known by the same surname as that baby's mum, which happens to be the surname of her husband, due to her becoming known by that surname, upon her marriage. The actual NSW form from those decades up to around the mid 1930s did not include a heading for the baby's surname. I am sure that the experienced UK RChatters familiar with GRO records will know if GRO birth certificates have a separate column heading for the baby's own surname.
So, in NSW records : If mum is not married to the baby's dad but dad acknowledges that he is the father, then both surnames are included in the registration under different column headings, (mother's details, and father's details) so both parents' surnames are indexed, but only ONE birth is registered. If mum does not have the dad's express permission to name him on the registration, then the index will only list her surname. There is provision in NSW for later endorsements. These often need serious legal actions to alter the original information. NSW BDM online birth index is free to search, and it includes spelling variations eg Mc and Mac are often separately indexed, and hyphenated surnames are often indexed under BOTH

The obvious way to learn what is actually on a record (as opposed to an index) is to obtain a copy of the record itself. I use the word 'record' to refer to the actual document, the birth certificate. Perhaps the OP is using the word 'record' to refer to the index.
Cheers, JM
Hi, I have three people with more than one birth record on FreeBMD/GRO. ....... The 1923 records have a hand-written correction/ addition, again for both family names. So, in this instance there are four records! How legal is/ was this to have both names recorded for the same person? .....